Portfolio (Portfolio C) Feasible set or opportunity set represented by the curved line AB The curve bends backwards. Investors invest above MVP.

Effect of Correlation on Diversification

O r = -1

r=0

r=1

Effect of Correlation on Diversification

Markowitz Efficient Frontier (Multiple Securities)

The efficient frontier represents the set of portfolios that will give the highest return at each level of risk or the lowest risk for each level of return.

Efficient Portfolio A portfolio is efficient if there is no alternative with: Higher expected return with same level of risk Same expected return with lower level of risk Higher expected return for lower level of risk

Adding Risk-free Asset

Adding a risk-free asset can change the efficient frontier as it has no risk/variance.

Capital Allocation Line

CAL

R E(Rm)

P Rf

= + =

Capital Allocation Line

Y = MX + C ( ) = +

CALR E(Rm)

P Rf

Risk Aversion Risk aversion refers to the behaviour of investor to prefer

less risk to more risk.

Risk averse investors: Prefer lower to higher risk for a given level of expected return Accept high risk investment only if expected returns are greater

Risk Aversion (Different Investors)

E(R)

Risk Neutral Investor

Risk

Risk Aversion (Different Investors)

E(R) IP IQ

Risk Averse Investors

Risk Neutral Investor

Risk

Risk Aversion (Different Investors)

E(R) IP IQ

Risk Averse Investors

Risk Neutral Investor Risk Lovers

Risk

Utility Indifference Curve

U = E(R) A * Variance U is a given level of happiness A is the level of risk averseness